This application claims a priority from German patent application No. 100 39 666.6, filed Aug. 14, 2000, and the contents of that application are incorporate herein by reference.
This invention relates to a method and an apparatus for estimating the frequency and/or phase of a digital signal.
A method of estimating frequency is disclosed by J. K. Wolf and J. W. Schwartz, “Comparison of Estimators for Frequency Offset,” IEEE Transactions on Communications, vol. 38, no. 1, January 1990, pages 124-127. It is proposed in this article that the phase of a complex digital input signal be differentiated and that the differentiated phase be fed to an averaging filter. This article shows that the ideal pulse response of the averaging filter is parabolic. The parabolic curve of the pulse response of the averaging filter can be approximated relatively well by a trapezoidal curve with an increasing range, a constant range and a descending range. The standard deviation of the estimation error increases by only about 6% in comparison with using the ideal averaging filter with the parabolic pulse response. Therefore, this could be termed a sub-optimal frequency estimator.
If the filter with the trapezoidal pulse response mentioned in the above article were to be implemented directly, a relatively large number of multiplications would have to be performed because each sample value within an observation interval must be multiplied by a corresponding coefficient.
Therefore, it is an object of this invention to provide a method and an apparatus for estimating the frequency and/or the phase of a digital input signal, which preferably works without logic-gate-intensive multipliers.